Computer-aided design (CAD) software allows a user to construct and manipulate complex three-dimensional (3D) models. A number of different modeling techniques can be used to create a 3D model. These techniques include solid modeling, wire-frame modeling, and surface modeling. Solid modeling techniques provide for topological 3D models, where the 3D model is a collection of interconnected topological entities (e.g., vertices, edges, and faces). The topological entities have corresponding supporting geometrical entities (e.g., points, trimmed curves, and trimmed surfaces). The trimmed surfaces correspond to the topological faces bounded by the edges. Wire-frame modeling techniques, on the other hand, can be used to represent a model as a collection of simple 3D lines, whereas surface modeling can be used to represent a model as a collection of exterior surfaces. CAD systems may combine these and other modeling techniques, such as parametric modeling techniques. Parametric modeling techniques can be used to define various parameters for different features and components of a model, and to define relationships between those features and components based on relationships between the various parameters.
CAD systems may also support two-dimensional (2D) objects, which are 2D representations of 3D objects. Two- and three-dimensional objects are useful during different stages of a design process. Three-dimensional representations of a model are commonly used to visualize a model in a physical context because the designer can manipulate the model in 3D space and can visualize the model from any conceivable viewpoint. Two-dimensional representations of a model are commonly used to prepare and formally document the design of a model.
CAD systems may display tolerance information to describe manufacturing parameters for a model. Tolerance information may specify allowable deviations in a feature from specified dimensions or locations. For example, a plus/minus tolerance specification can indicate an allowable positional deviation of a feature in a manufactured part.
Design and manufacturing engineers may need to know the minimum and maximum values for an assembly dimension to ensure that the assembly once manufactured will function as designed. Typically, the minimum and maximum dimensions are dependent upon the order in which parts are mated in an assembly and the numerous tolerance values throughout the assembly.
The minimum and maximum condition may be computed manually. To manually calculate the minimum and maximum tolerances, for each tolerance in the assembly, the engineer determines the minimum and maximum condition and the impact of these conditions on other features and parts in the assembly. Manually calculating the minimum and maximum tolerances can be a laborious task.
Commercially available tolerance analysis software that automatically calculates minimum and maximum tolerances exists. A common computerized technique for performing tolerance analysis is based on Monte Carlo simulation. This technique creates a simulation model for each feature in the assembly based upon the applied tolerances. For numerous iterations, exact values for the plus/minus tolerances are randomly selected and the resultant values for assembly dimensions of interest are tracked. Monte Carlo simulation statistically determines the probability of various values for the dimensions of interest. The speed of a Monte Carlo simulation depends upon the size of the model, the number of tolerances, the number of iterations, and available computing resources, among other parameters. To be most effective, Monte Carlo simulation generally requires engineers to have an expertise in the field of tolerance simulation and statistics.
Another computerized tolerance analysis technique is based upon kinematics linkages. Constraints are assigned and are based upon the tolerances that have been applied to the tolerance features in an assembly. The kinematics model is then manipulated to determine the possible values for the assembly dimensions. While not suffering from performance problems, in general, the kinematics linkages technique does not solve for the complete breadth of the ASME Y14.5M and ISO 1101 tolerance standards.
A 3D CAD system that can rapidly compute the minimum and maximum conditions of an assembly based on applied tolerances as well as the root sum squared (RSS) values, does not need to involve a simulation expert to analyze tolerances, and implements the ASME Y14.5 and ISO 1101 standards would enhance the capabilities and ease of use of a 3D CAD system.